Question

1. ab⊥cd

in this diagram, line segment cd is the perpendicular bisector of line segment ab. assume the conjecture that the set of points equidistant from a and b is the perpendicular bisector of ab is true. is point m closer to point a, closer to point b, or the same distance from both points? explain how you know.

Explanation:

Step1: Recall the property of perpendicular bisector

The perpendicular bisector of a line - segment is the set of all points that are equidistant from the endpoints of the line - segment.

Step2: Identify the position of point M

Point M lies on the perpendicular bisector CD of line segment AB.

Answer:

Point M is the same distance from both points A and B because it lies on the perpendicular bisector of AB, and by the property of the perpendicular bisector, any point on it is equidistant from the endpoints of the line - segment it bisects.